Model independent extraction of the proton magnetic radius from electron scattering

TL;DR

This paper presents a model-independent method combining analyticity constraints with scattering data to accurately determine the proton magnetic radius, also assessing the impact of additional neutron and pion data.

Contribution

It introduces a novel approach that avoids model-dependent assumptions for extracting the proton magnetic radius from scattering data.

Findings

Proton magnetic radius is approximately 0.87 fm with combined data.

Including neutron and pion data refines the radius estimate.

Neutron magnetic radius is estimated at about 0.89 fm.

Abstract

We combine constraints from analyticity with experimental electron-proton scattering data to determine the proton magnetic radius without model-dependent assumptions on the shape of the form factor. We also study the impact of including electron-neutron scattering data, and $\pi\pi\to N\bar{N}$ data. Using representative datasets we find for a cut of $Q^2\leq0.5$ GeV$^2$, $r_M^p=0.91^{+0.03}_{-0.06}\pm0.02$ fm using just proton scattering data; $r_M^p=0.87^{+0.04}_{-0.05}\pm0.01$ fm adding neutron data; and $r_M^p=0.87^{+0.02}_{-0.02}$ fm adding $\pi\pi$ data. We also extract the neutron magnetic radius from these data sets obtaining $r_M^n=0.89^{+0.03}_{-0.03}$ fm from the combined proton, neutron, and $\pi\pi$ data.